Strength Reduction Technique Research Articles

Stability Assessment of Multi-Stage Slopes Considering Local Failure

The analytical method for slope stability analysis requires a collapse mechanism in advance. The collapse mechanism for a multi-staged slope is generally assumed to be overall failure, whereas this kind of slope may suffer from local failure. However, a local failure is rarely reported in the previous research for multi-staged slopes, which may result in an overestimate for slope stability. To this end, local failure is incorporated into the collapse mechanism for the first time, so as to develop a complete approach to assess the stability of multi-stage slopes. The modified pseudo-dynamic method is conducted to properly account for seismic effects. Thanks to the limit analysis method and strength reduction technique, the safety factor of a multi-stage slope is obtained. The result obtained by the presented approach shows a good agreement with that of previous literature and numerical calculations. The collapse mechanism of multi-stage slopes is studied, and the safety factor is presented schematically for a wide range of parameters. The results show that the local failure for a multi-stage slope often manifests under the intense seismic effects.

Another look at the stability of unsaturated soil slopes considering nonuniformity and nonlinearity

Natural soils in site are mainly unsaturated under evaporation or infiltration effects, which cause nonuniformity along depth or present nonlinearity in strength properties even for uniform soil strata. Conventional upper-bound analysis is unable to handle the above issues, requiring alternative approach such as the discretization-based kinematic analysis to be adopted. Nonlinear matric suction profile along depth is theoretically formulated under one-dimensional steady flow. Within the context of extended Mohr Coulomb (MC) failure criterion, total cohesion is explicitly expressed for unsaturated soils. Meanwhile, an extended Power-law failure criterion is proposed to consider nonlinear characteristics of uniform soils in unsaturated zones. Based on these two failure criteria, upper-bound analyses of unsaturated clay slopes’ stability are evaluated by slope safety factor (FoS). Optimal upper-bound FoS solutions are sought by a strength reduction technique and iterative algorithm. Effects of clayey soils’ non-uniformity, nonlinearity and some other influential factors on unsaturated slope stability are investigated, which is of engineering significance for sound design and reliable assessment of unsaturated slopes. One of key findings is that stability of unsaturated soil slopes enhanced by their unsaturated soil strength is substantial and should be utilized to derive a more economical design or construction of temporary slopes in practice.

Stability analysis of a free-standing backfill wall and a predictive equation for estimating the required strength of a backfill material - a numerical modelling approach

Cemented backfilling has enabled underground hard rock mines to extract orebodies more safely with improved ore recovery. It is important to estimate the minimum required strength parameters for a backfill mix by optimizing the binder percentage to enable cost-effective and safe stoping operations. We conducted three-dimensional numerical modelling to study the effect of various stoping parameters on the stability of a free-standing backfill wall. A Mohr-Coulomb material model was used for the backfill material and the rock-fill interface. A strength reduction technique, excluding friction angle, was employed to arrive at a minimum stable strength value for the backfill. For a given combination of strength values, the stability state of the backfill wall could be demarcated using a displacement and yield zone tracking method. The numerical modelling results are compared to some earlier theoretical models. From the simulations, a predictive equation is developed to predict the required strength parameters for a backfill mix to ensure a stable free-standing wall. Examples are given of the successful use of the predictive equation at some underground hard rock mine sites in India.

Estimating the Optimal Overall Slope Angle of Open-Pit Mines with Probabilistic Analysis

Slope instability of open-pit mines has adverse impacts on the overall mine profitability, safety and environment. The slope of an open-pit mine is crucially influenced by the slope geometry, quality of rock mass and presence of geological features and their properties. The objective of this study is to demonstrate a method to select the optimal overall slope angle of open-pit mines according to three design parameters, namely, safety (e.g., probability of instability), productivity (e.g., profit) and mining costs (e.g., cost of removal of overburden). Therefore, this study attempts a hybrid approach in which numerical modelling is integrated with probabilistic analysis to evaluate the stability of an open-pit mine at various overall slope angles. Two-dimensional elasto-plastic finite-element, RS2D, has been used to develop a series of models at different ultimate slope angles employing shear strength reduction technique (SSRT). Li’s point-estimate method of n3 has been invoked in deterministic analysis to tackle the inherent uncertainty associated with host rock mass properties. The results reveal that the mine profitability increases and the cost of overburden removal decreases as overall slope angle becomes steeper. However, the slope stability deteriorates. Therefore, it is highly advisable to combine these three design parameters (e.g., safety, productivity, and cost) together when selecting overall slope angle of open-pit mines.

Three-dimensional tunnel face stability considering slurry pressure transfer mechanisms

In slurry-shield tunneling, the bentonite slurry tends to infiltrate into the soil skeleton ahead of the tunnel face, causing a forward seepage flow associated with excess pore pressures in the ground. Both the slurry infiltration and the forward seepage flow significantly impact the tunnel face stability. In the present paper, a kinematic approach of limit analysis with the classical three-dimensional discretized rotational failure mechanism is employed to assess the face stability of a slurry-shield-driven tunnel. Three situations of slurry infiltrations that influence the face pressure transfer mechanisms were considered: a full filter cake, a penetration zone, and pure groundwater flow without a filter cake or a penetration zone. The pore pressure distributions surrounding the tunnel face were firstly obtained using numerical calculations. Afterward, the incorporation of numerically obtained pore pressure distributions into the work rate calculations allows considering a three-dimensional forward seepage flow ahead of the tunnel face, which provides a rigorous upper-bound estimation to the tunnel face safety factor determined by the strength reduction technique. The proposed method is validated by comparing the calculated results with those provided by previously published literature. The effects of excess slurry pressures, hydraulic conditions, pressure drop coefficients, and soil shear strength were investigated. Several design charts are given for practical application.

Stability assessment of soil-nailed slopes using the homogenisation approach

This study aims to evaluate the stability of the soil-nailed slope using an improved discretisation-based failure model in the framework of the upper-bound limit analysis theorem and the homogenisation approach. The improved discretisation-based failure model generated from the slope crest is first proposed by using the discretisation technique. Based on the homogenisation approach, a failure criterion for reinforced soils is established with considering the possible tensile failure and pull-out failure of soil nails. The proposed failure criterion is then incorporated into the improved slope failure model to determine the factor of safety (FoS) of the reinforced slope by using a method integrated the upper-bound limit analysis theorem and the strength reduction technique. The proposed method is validated by comparing with existing solutions and numerical results, showing that the proposed method is an effective approach to investigate the stability of reinforced slopes, especially for the cases with high reinforcement density. The effects of model parameters on the slope stability are finally presented.

A new method for defining the local factor of safety based on displacement isosurfaces to assess slope stability

Slope stability is mainly assessed by the factor of safety (FS) parameter. As an improvement to the integral FS derived from the conventional limit equilibrium method (LEM), the local factor of safety (local FS) is used to describe the FS of each material element. However, although current slope stability algorithms with LEM rely on only strength criteria, some areas of a slope show almost no displacement, even though plastic yielding is occurring within the slope. For these reasons, we developed a new approach for defining the local FS based on the displacement isosurface. Adopting the Mohr–Coulomb (M–C) strength criterion, this new algorithm calculates the local FS in the potential sliding zone with a change in the apparent displacement. Based on the shear strength reduction technique, the distributions of the local FS within 2D homogeneous slopes with different shear strengths and within a real 3D slope with a complex topography are analyzed. Firstly, the applicability of the new approach was examined and we found that the local FS decreases significantly only when the direction of the yielding surface approaches the displacement direction, which also reveals that the LEM may underestimate the FS. In addition, the areas of a slope where the local FS strongly changes depend on the slope geometry and also control the instability patterns. Further, the results of a local FS in a 3D slope analysis show that complex topography and internal structure can cause the alternation of stable and unstable blocks in the slope and that the mobilities of the blocks induced by the instability differ in different areas. Finally, some local optimized retaining countermeasures were successfully implemented for supporting a real engineering slope guided by the local FS. Our results indicate that this improved algorithm can provide a more suitable and accurate local FS with which to assess slope stability and reveal more realistic instability patterns than approaches using the integral FS.

Geometrical profile of cohesive-frictional soil slopes for optimal stability

: In this study, finite element method with strength reduction technique is employed to study the stability of slopes with non-straight line profiles comprises three segments. According to this method, the strength parameters are reduced until the slope becomes on the verge of failure. A software called (Optum G2) is used to analyze the geometrical and mechanical parameters. The effect of the geometrical shape of the slope with specific limitations on the factor of safety (FOS) has been investigated to find the corresponding profile configuration that provides maximum stability. The profile (slope face geometry) has been divided into three straight lines (segments) with different lengths. The study involved the soil cohesion (c), angel of internal friction (∅) and the angle of the imaginary straight line linking the slope toe with slope crest (β) called herein slope inclination. The main results showed that using the three segments facing profile can increase the factor of safety (FOS) by up to 15% in comparison with the corresponding slopes of straight line profile. Design charts has been introduced to be utilized by engineers and practitioners to obtain the geometrical parameters for the optimal profile as well as the expected improvement percentage in factor of safety.

Environmental Protection Measures Against Landslides Impacts Caused by Slope Instability

Each slope is affected by the variations of slope gradient combined with the driving forces including the groundwater action, producing shear stresses in the slopes, which are contradicted by the soil shear strength. The slopes instability may cause the displacement of the mass of soil downstream recognised as landslide. Consequently, landslides are one of the most significant catastrophic phenomena observed on the earth surface. This phenomenon can be considered as a major concern on the social and economic point of view and for the quality of life of a local population, including also the environmental impact on the ground water level, blockage of rivers, road destruction, forests and ecosystems destruction, etc. The current study makes the usage of the shear strength reduction technique to evaluate the stability of slopes. This process has tendency to reduce shear strength as rarer as failure is produced. This study is achieved along with pseudostatic and static methodologies. Varied parameters influence on the stability of slopes are revealed by accomplishment of many studies. To end, the Static method findings are acceded to comparison with the ones found by Pseudo-Static method.

Estimating the Basal Heave Stability of Narrow Braced Excavations

Engineering practices indicate that narrow braced excavation exhibits a clear size effect. However, the slip circle method in the design codes fails to consider the effect of excavation width on basal heave stability, causing waste for narrow excavation. In this paper, numerical simulation for basal heave failure of excavation with different widths was performed by FEM with SSRT (shear strength reduction technique). The results revealed that the failure mechanism of narrow excavation is different from the complete slip circle mode. In addition, the safety factor decreases increasingly slowly as the excavation widens and stabilizes when approaching the critical width. Subsequently, the corresponding computation model was presented, and an improved SCM (slip circle method) was further developed. Finally, the engineering case illustrated that it can effectively optimize the design, which exhibits clear superiority.

Correlations of geotechnical monitoring data in open pit slope back-analysis -A mine case study

Geotechnical monitoring plays an important role in the detection of operational safety issues in the slopes of open pits. Currently, monitoring companies offer several solutions involving robust technologies that boast highly reliable data and the ability to control risky conditions. The monitoring data must be processed and analysed so as to allow the results to be used for several purposes, thereby providing information that can be used to manage operational actions and optimize mining plans or engineering projects. In this work we analysed monitoring data (pore pressure and displacement) and its correlation with the tension and displacement of the mass of an established failure slope calculated using the finite element method. To optimize the back-analysis, a Python language routine was developed using input data (point coordinates, parameter matrix, and critical section) to use software with the rock mass parameters (cohesion, friction angle, Young's modulus, and Poisson's ratio). For the back-analysis, the Mohr-Coulomb criterion was applied with the shear strength reduction technique to obtain the strength reduction factor. The results were consistent with both the measured displacements and the maximum deformation contours, revealing the possible failure mechanism, allowing the strength parameters to be calibrated according to the slope failure conditions, and providing information about the contribution of each variable (parameter) to the slope failure in the study area.

Optimisation of a Slope-Stabilisation System Combining Gabion-Faced Geogrid-Reinforced Retaining Wall with Embedded Piles

Slope instability is a common geotechnical issue in South Gippsland, Victoria, Australia. The network of rural roads constructed and maintained by the local authority are greatly affected by the instability. An integrated slope-stabilisation system that combines two well-developed slope stabilisation methods has been used widely in this district. These two methods are gabion-faced geogrid-reinforced retaining wall and pile retaining structures. These two methods are connected by a steel rail that is welded at the top of the piles to buttress the lowest row of the gabion basket wall. In order to reflect the site conditions accurately, a three-dimensional non-linear finite element approach is adopted in this study. The elastic-perfectly plastic constitutive model with the Mohr-Coulomb yield criterion is used to describe the behaviour of the soil and the gabion basket. With the assistance of the shear strength reduction technique, the effectiveness of the integrated system is demonstrated through the comparison of the representative indicators of the slope stability among various slope configurations. A series of parametric studies related to the ratio of the embedded length of geogrid to the height of the slope, the ratio of the embedded length of the pile to the thickness of the unstable soil layer, and the ratio of the spacing to the diameter of the pile have also been conducted for the purpose of optimising this slope stabilisation infrastructure. The results from the parametric studies indicate that the optimised and improved integrated infrastructure can stabilise the road and slope economically without the loss of the safety margin.

Computational tools for the analysis of circular failure of rock slopes

Among other types of failure in slopes created by excavation or filling, circular (also referred to as rotational) type of failure plays an important role in the design and stability analysis of high rock slopes, such as those encountered in deep open pit mines. When a rock slope of significant height involves predominantly one type of jointed rock mass, the scale of the problem is frequently such that the rock mass (intact rock and rock discontinuities) can be regarded as a homogeneous isotropic material. In such case, if the rock slope is unstable and collapse occurs, circular (or rotational) failure as in failed slopes in soils is also observed for the rock slope. One main goal in practical design of deep open pit mines is to determine safe inclination angles for the pit faces to be excavated to avoid failure. Computational tools for quick assessment of the stability conditions, in particular determination of factor of safety and location of the critical circular failure surface, are useful during the preliminary stages of open pit design. Among others, such tools allow the engineer to gain insight in the role that the different variables controlling the problem have in defining the stability conditions for the rock slope. This paper provides first an overview of typical numerical techniques used to assess the stability of high rock slopes. For the case of slopes in rock masses that are assumed to obey the Mohr-Coulomb or the Hoek-Brown failure criteria, the paper discusses how application of transformation rules leads the criteria to be re-casted in dimensionless form, so when these are applied to the solution of slope problems, the results (factor of safety and coordinates that define the location of the critical circular failure surface) can be summarized in dimensionless compact forms. The paper presents then computational tools in the form of dimensionless charts and computer spreadsheets for stability analysis. These are developed from numerical limit equilibrium models that use the mentioned transformation rules. Among others, the computational tools allow the concept of mechanical similarity of rock slopes to be naturally introduced. Finally, the paper presents various rock slope examples that illustrate the use of the computational tools. In these examples, results from limit equilibrium models are also compared with results obtained with full numerical analysis, in particular with finite difference models implementing the shear strength reduction technique.

Slope stability of deep surface coal mines in the presence of a weak zone

Coal and lignite (brown coal) are geo-resources that govern energy production for decades. Geomechanical challenges, particularly slope stability, related to surface coal and lignite mines are critical during operation and determine the post-coal era. Several failure incidents have been reported in mining areas, typically associated with a sub-horizontal failure surface on a weak—clay or marl—layer or an interface of low strength. This weak zone controls the soil profile in terms of stability and is common in several mines globally. In this work, the finite element method with the shear strength reduction technique is primarily employed to evaluate the slope stability of this profile. Three geotechnical software are initially compared, and results are identified as practically identical. Moreover, slopes with benches, as typically in mines, and without benches, as typically in slope stability analysis, are compared, with the no-benches analysis being consistently more conservative. The crucial parameters' effect is then examined: the height and the inclination of the slope, the inclination, thickness, and strength of the weak zone, and the strength of the overburden soil. Their effect on slope stability is quantified by combining the probabilistic point estimate method with the finite element method. It is concluded that the inclination and strength of the weak zone and the water conditions are the most critical parameters and control the stability. This work can support a preliminary slope stability analysis and expands the knowledge and understanding of slope stability of a weak zone profile.

2-D soil slope-stability evaluation using vector-sum method

Over the stress state of the sliding body artificially assumed in Limit equilibrium method, the real stress state from any numerical analysis can be imported into a limit equilibrium analysis where the normal stress and shear stress are computed with respect to any selected slip surface. Considering the vector characteristics of force and the strength reduction definition, vector sum method by strength reduction technique was proposed, in which the factor of safety (FOS) can be directly calculated by the force and moment equilibrium. Finally, numerical experiments with six possible conditions are used to verify this proposed method, and the results show that the FOS obtained by the proposed method is in good agreement with the average FOS by limit equilibrium methods.

Reliability-based prediction of landslide using efficient Monte Carlo Simulation

Several studies have attempted to develop thresholds for prediction of landslide initiation due to antecedent rainfall by using the physical-based approach. The approach offers a better understanding of the underlying process of the landslide mechanism. In the previous studies, however, determinate values of hydro-mechanical soil parameters are commonly considered, neglecting the uncertainties of the variables. Thus, this study aims to propose a relatively computationally, inexpensive reliability approach to address the uncertainties of the multivariate. The application of the proposed model is demonstrated by taking a case study from Sabah, Malaysia. The Latin Hypercube Sampling was adopted for efficient sampling, while the dependencies of the multivariate were modelled using a higher-order copula. The infiltration process and slope stability were assessed based on a fully-coupled seepage-deformation and shear strength reduction technique, respectively in a finite element programme. The probabilities of failure for various antecedent rainfall condition were computed by using Monte Carlo Simulation. In order to reduce the computational cost of the simulation, the Multilayer Perceptron regressor was applied to form the non-linear surrogate model for an implicit limit state function.

Stability of a 3D unsaturated vertical cut slope subjected to variable rainfall infiltration

Rainfall infiltration is one of the main triggers of slope failure. Based on the upper bound theorem of limit analysis, this work presents an analytical stability analysis of a 3D vertical cut slope subjected to rainfall infiltration. An analytical model that can directly provide pore water pressure change at any depth and time is adopted to calculate the time-dependent matric suction and shear strength of unsaturated soil during the rainfall infiltration process. Thereafter, based on a 3D rotational failure mechanism of a slope, the energy balance equation is built, and the factor of safety (FoS) of the slope is consequently determined in conjunction with the strength reduction technique. The influences of the 3D characteristics of the slope and rainfall patterns on both FoS and failure pattern of the slope are investigated. It is found that the 3D characteristic of slope is a key factor which determines the FoS of slope. Different rainfall infiltration patterns lead to diverse variation rules of both the FoS solutions and the critical failure patterns of slope. However, these rainfall patterns with a same accumulated rainfall result in the same FoS solution of slope at the end of rainfall infiltration. The present work may provide guidance on the stability analysis and preliminary design of slopes subjected to rainfall infiltration.

Three-Dimensional Face Stability of Tunnels in Unsaturated Soils with Nonlinear Soil Strength

Stability analysis of tunnel faces is usually carried out under dry or saturated assumptions. However, in practice, soils are often unsaturated due to the presence of matric suction, and unsaturated components often have nonnegligible effect on soil strength. For a more realistic solution, the influence of unsaturated components on the stability of a three-dimensional tunnel face was considered for the first time. To meet this requirement, the three-dimensional rotational failure mechanism and the extended form of Mohr–Coulomb failure criterion were used to express the face failure in the limit analysis framework. The strength reduction technique was employed to estimate the stability of ta hree-dimensional tunnel face and the safety factors were calculated by the bracketing method. The proposed method is verified by comparing with the results obtained by FLAC3D. The effects of matric suction distribution, tunnel geometry parameters and shear strength nonlinearity on the stability of three-dimensional tunnel face were analyzed in the parameter analysis. The results show that considering the effect of suction stress is beneficial for improving the tunnel face stability, but it is influenced by the matric suction distribution, the tunnel geometry, soil types, and the shear strength nonlinearity. The main novelty of this study is to develop an effective method to evaluate the face stability of tunnels in unsaturated soils.

Instability analysis of jointed rock slope subject to rainfall using DEM strength reduction technique

Uncertain climatic factors like rainfall can induce the complex hydro-chemo mechanical processes within the rock mass, and thus substantially increase the failure probability of rock slope. This paper presents a numerical investigation into the rainfall-induced instability mechanism of jointed rock slope with two joint inclinations of dipping 45° and 60° and the corresponded safety factor using the two-dimensional Distinct Element Method (DEM), where the non-uniform strength reduction approach is employed. For this purpose, some crucial aspects were mainly discussed, i.e. the quantifications of water softening and chemical weathering effects in the micro bond contact model, the necessary fitted functional relationships used in the safety factor, and determinations on the intensities of water softening and chemical weathering. The results show that the proposed DEM strength reduction provides a feasible approach to analyze the rainfall-triggered instability of jointed rock slope. The significant rise of bond breakage and the accompanied large displacement of sliding block indicate the achieved critical infiltration depth of rainfall and the consequent destabilization of jointed rock slope. The jointed rock slope with steeper dipping joints has lower safety factor, and thus is more prone to instability under the same rainfall effect.

Maximum safe freight train speed on railway embankments under rapid drawdown conditions based on coupled stress-seepage slope stability analysis

The rapid drawdown of the water level adjacent to a railway embankment can reduce its stability, which could compromise the safety of train movements. To investigate the effect drawdown on railway embankments as a function of train speed, a coupled finite element-based model was developed accounting for simultaneous deformations, stresses and seepage. To determine maximum safe train speeds, a comprehensive study was carried out that included slope parameters (e.g. railway embankment height, natural slope height, slope ratio), rapid drawdown ratios, and external freight train loads as a function of speed. The models used the shear strength reduction technique, in which the factor of safety for each model was obtained. Generally, steeper natural slopes with lower railway embankments built upon them are more prone to failure, thus severely limiting train movements when a drawdown condition occurs. However, for a large number of cases, mainly for flatter slopes, a safe passage can be achieved by limiting train speed, while tall railway embankments appear to be able to withstand drawdown conditions without a considerable reduction in train operating speeds. The results of findings are summarized in a table and it is hoped that the study will be useful to increase the safety of freight train operations, particularly in cases when there is a sudden change or an unusual event in the waterways adjacent to a railway embankment.